Plane Geometry - Bruce E. Shapiro

SECTION 38. THE PYTHAGOREAN THEOREM 199Figure 38.6: Bhaskara’s Proof of the Pythagorean Theorem.Figure 38.7: Proof by rearrangement of the Pythagorean Theorem.to cover a small a × a square (above the dashed line) and a larger b × bsquare (beneath the dashed line).Proof. Fifth Proof of the Pythagorean Theorem. See figure 38.7. Oneach side of the figure are two large squares, of size (a + b) × (a + b). On theleft, we see that this is equal to four times the area of the triangle plus thearea of the square on the hypoteneuse. On the right we see that this is equalto four times the area of the triangle plus the sum of the areas of the squareon each of the sides. Hence the area of the square on the hypoteneuse isequal to the sum of the areas of the squares on the sides.Revised: 18 Nov 2012 « CC BY-NC-ND 3.0.